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Question
A wheel of moment of inertia 0⋅500 kg-m2 and radius 20⋅0 cm is rotating about its axis at an angular speed of 20⋅0 rad/s. It picks up a stationary particle of mass 200 g at its edge. Find the new angular speed of the wheel.
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Solution
Given
Initial moment of inertia of the system,
I1 = 0.500 kg-m2;
r = 0.2 m;
ω = 20 rad/s
Mass of the stationary particle, m = 0.2 kg
Final moment of inertia of the system,
I2 = I1 + mr2
It is given
External torque = 0
Angular momentum is conserved; therefore, we have
\[I_1 \omega_1 = I_2 \omega_2\]
\[\Rightarrow 0 . 5 \times 20 = \left( 0 . 5 + 0 . 2 \times \left( 0 . 2 \right)^2 \right) \omega_2 \]
\[ \Rightarrow \omega_2 = \frac{10}{0 . 508} \approx 19 . 7\text{ rad/s}\]
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